I think that you are right to question your sister's condemnation of "neither of us are", but wrong to say that "one of us" cannot take third-person agreement because of the presence of the first-person pronoun "us".
Consider the sentence "One of us is wrong." Would you say that this is incorrect because we can't say "We is wrong?" It turns out that people do say "one of us is" and not *"one of us are" (or *"one of us am"), so it seems clear that the grammatical person of the pronoun after "of" doesn't always affect the person agreement used with the verb.
I think speakers who use "neither of us are" are using plural agreement with "neither". This seems to be grammatical for many, perhaps most speakers, but I think that it has been criticized for the same reasons "none of them are" has been criticized. Interestingly, plural agreement does seem to also be used by some speakers for the positive pronoun "either", in contexts like "if either are".